Is it normal to be gaining weight as you grow?

I'm 13, and I was shirtless and mii amiga tellss me meli you getting fat and I have realized that I've been eating more and I get hungry more often and eat bigger meals. but Im 5'1" and I weigh 83 ten it goes up to 93 then in between. this is how it always is I'm dropping and gaining all the time. I don't throw it up or anything. is it normal?